There is considerable interest in using rare earth doped fibers to amplify weak optical signals for both local and trunk optical telecommunications networks. The rare earth doped optical amplifying fibers are low cost, have low noise properties, have a relatively large bandwidth which is not polarization dependent, have no crosstalk problems, and have relatively low insertion losses at the wavelengths which are used in optical communications. In use, rare earth doped optical fiber amplifiers are coupled end-to-end to an optical communication fiber and are normally transversely coupled, through a directional coupler to a laser diode pump so that a weak optical input signal at some wavelength within the rare earth doped optical fiber amplifer experiences a gain. The directional coupler is designed to have a high coupling ratio at the pump wavelength and low coupling ratio at the signal wavelength. The pump light may be made to propagate either co-directionally or contra-directionally with respect to the signal, according to whether the unconverted pump light can be more conveniently filtered at the transmitter or the receiver. The core diameters and refractive index profiles determines the mode sizes of the undoped transmission fiber and of the doped amplifying fiber and, therefore, the fibers will not necessarily be the same. In the transmission fiber the primary constraint is the requirement of waveguide dispersion while in the amplifying fiber there exists the need to maximize the overlap of the pump and signal modes. Because the amplifying fiber can have a mode size which is different from that of the transmission fiber, the losses at the splice due to mode mismatch can be quite large. To reduce this loss at the core-to-core splice between the two fibers, it has been proposed that the fusion splice be tapered.